Question 596156
Hi, there--
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We can model this problem with a right triangle. One leg of the triangle runs horizontally along the ground; its length is the distance from the bottom of the ladder to the house.
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The other leg runs vertically along the wall of the house from the ground to the base of the window; we know its length is 12 feet.
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The hypotenuse of the triangle is the ladder itself. We know that the ladder is 13 feet long.
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We want to find the distance from the base of the ladder to the house, length of the first leg. Let's call b the length of this leg. Since we have a right triangle, we can use the Pythagorean Equation. The variables, a and b, are the legs of the right triangle, and c is the length of the hypotenuse.
{{{a^2+b^2=c^2}}}
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Substitute our known values into the equation and solve for b.
{{{12^2+b^2=13^2}}}
{{{144+b^2=169}}}
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Subtract 144 from both sides.
{{{b^2=169-144}}}
{{{b^2=25}}}
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Take the square root of both sides. Since 5*5=25, b=5.
{{{b=5}}}
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Roger should place the bottom of the ladder 5 feet from the house.
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That's it. Feel free to email is you still have Qs.
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Ms.Figgy
math.in.the.vortex@gmail.com